Gabriel Vilardi and Blake Lizotte each had a goal and an assist, Pheonix Copley made 27 saves in his fourth straight victory and the Kings (19-12-5) extended their winning streak to four games.
"Calgary is a good team, they didn't go away," Lizotte said. "Good resiliency from our group, kind of letting them back in the game -- and rightfully so, they made some good plays -- but for us to kind of regroup and win that game in overtime is huge."
Tyler Toffoli and Dillon Dube scored in the third period for the Flames (15-12-7), who earned a point in their fifth straight road game (2-0-3). Dan Vladar made 28 saves.
"There's no doubt in our minds that we could come back," Toffoli said. "It was just a matter of putting in the work and staying with it."
Phillip Danault put Los Angeles ahead 2-1 at 1:29 of the third when he scored on a backhand shot, faking out Vladar after an aggressive forecheck by Alex Iafallo forced a turnover in the offensive zone.
Lizotte made it 3-1 just 10 seconds later at 1:39, putting in Vilardi's rebound from the high slot.
"With Arvy and 'Gabe's' skill level, it makes it easier for me to play," Lizotte said. "I can create havoc out there and play with speed and kind of create time for them. They make good plays, so my goal is just to give them the most time possible with the puck."